Uncertainty Analysis
= Uncertain Systems = * Bounding the Dynamic Behavior of an Uncertain System via Polynomial Chaos-based Simulation = Interval Arithmetic = * Should we be concerned about round-off error?: There are several extensions or libraries in the FORTRAN, Pascal, and the C++ programming languages with facilities for ¯xed or arbitrary precision interval arithmetic 1,2. In addition, Maple V version 2 and Mathematica version 2.2 provide for "range" and "Interval" arithmetic, respectively. However, the "range" arithmetic in Maple V version 2 (using evalr()) does not seem to do outward rounding (or outward-rounded I/O) properly. For this reason, Maple was not able to provide guaranteed "traps" for several interval computations tested. * Some disasters attributable to bad numerical computing * Tutorial on Verified Scientific Computing * Lecture Notes * Interval Computations * Interval arithmetic - Wikipedia, the free encyclopedia * Computer Algebra Systems * ROA Using Interval Arithmetic * Interval and Related Software * Interval analysis and computation * www.interval-methods.de * Applied Interval Analysis * Interval Arithmetic: Interval type and basic interval operations-V1.2 - Application Center * Applied Interval Analysis * Interval Computations: Introduction, Uses, and Resources * interval.louisiana.edu Global Optimization * Global Optimization Methods based on Interval analysis Books * Applied Interval Analysis * Interval Methods for Circuit Analysis * Introduction to Interval Analysis - lnk * Robust Model-Based Fault Diagnosis For Dynamic Systems * Applications of Interval Computations * Interval Methods for Systems of Equations * Global Optimization Using Interval Analysis Theses * GPU Accelerated Parameter Estimation by Global Optimization using Interval Analysis Interval Transfer Function * Model Order Reduction of Interval Systems Inequalities * SOLVABILITY OF SYSTEMS OF LINEAR INTERVAL EQUATIONS * Checking solvability of systems of interval linear equations and inequalities via mixed integer programming * Sergiy Butenko Implementation * Interval Arithmetic: Python Implementation and Applications Applications * Interval Computations Introduction Uses and Resources Circuit Analysis * Interval methods for analog circuits * A comparison of interval methods in symbolic circuit analysis applications * Interval methods for analog circuits * Interval Methods for Circuit Analysis * Interval Analysis of Linear Analog Circuits * Combination of Symbolic and Interval-Numeric Methods for Analysis of Analog Circuits * AUTOMATIC COMPUTATION OF A LINEAR INTERVAL ENCLOSURE * Lubomir V. Kolev * Reliable Computing * Interval Arithmetic for the Design of Electrical Engineering Systems = Affine Arithmetic = * Affine Arithmetic * Libaffa * ASOL = Taylor Models = * Approximations polynomiales rigoureuses et applications * Modern Map Methods in Particle Beam Physics (Chapter 2) * Taylor models and other validated functional inclusion methods * Using Taylor Models in Reachability Analysis of Nonlinear Hybrid Systems * Taylor Model Based Integration * Computation and Application of Taylor Polynomials with Interval Remainder Bounds * Benoit's Slides 2011 * Rigorous Polynomial Approximations and Applications * Verified Computations with Taylor Model Using Symbolic Algebra * Verified Methods * Introduction to Validated Computing Implementation * TAYLOR MODELS AND OTHER VALIDATED FUNCTIONAL INCLUSION METHODS * Bounding roundoff errors in Taylor models arithmetic * Bernstein Polynomials Algebraic Equations * Veriﬁcation of Invertibility of Complicated Functions over Large Domains * Rigorous Numerical Analysis with High-Order Taylor Models * Uncertainties in the solutions to boundary element method: an interval approach * Modified-accelerated Krawczyk’s algorithm * INTERVAL OPERATORS AND FIXED IKTERVALS * Algorithms for Verified Linear Algebra Verifying the solution of a linear system * The Krawczyk Algorithm: Rigorous Bounds for Linear Equation Solution on an FPGA * Real Root Isolation of Polynomial Equations Based on Hybrid Computation Inverse Taylor Model * Verified High-Order Inversion of Functional Dependencies and Interval Newton Methods * Verification of Invertibility of Complicated Functions over Large Domains Solving ODE * Interval Methods and Taylor Model Methods for ODEs * Taylor Model Flowpipe Construction * Rigorous Integration of Flows and ODEs using Taylor Models * Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: Long-term Stabilization by Shrink Wrapping * Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: Long-term Stabilization by Preconditioning * Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: The Single Step * Rigorous Analysis of Nonlinear Motion in Particle Accelerators * Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models * A Rigorous ODE Solver and Smale’s 14th Problem Picard Operator * A good example Implicit DAEs * Computing Validated Solutions of Implicit Differential Equations * Eﬃcient high-order methods for ODEs and DAEs * Rigorous Numerical Analysis with High-Order Taylor Models Applications * Graphical Algorithms * Continuous Collision Detection Workshops * SWIM 2013 * SWIM 2012 * SWIM 2011 * SWIM 2010 * SWIM 2009 * SWIM 2008 = Chebychev Models = * Rigorous Computation with Function Enclosures in Chebyshev Basis * VERICOMP * Chebychev Interpolations Model = Ellipsoids = * Trajectory Enclosures for Nonlinear Systems with Uncertain Initial Conditions and Parameters = The Inverse Problem for ODEs = * Solving the Inverse Problem for ODES Using the Picard Contraction Mapping * Picard Operator = Books = * Modeling, Design, and Simulation of Systems with Uncertainties * Applied Interval Analysis * Introduction to Interval Analysis = People = * Martin Berz and Kyoko Makino * Nedialkov * Sriram Sankaranarayanan * Bruce Krugh(CMU) * Zhi Han * Jiri Rohn * Interval Analysis and its Applications * Interval Computations * Alexander Gofen (Analytical Continuation, ODE's and Automatic Differentiation Unified) * Mark A. Stadtherr * Stig Skelboe = Tools = * OptiY * COSY * DAETS * VNODE * INTLAB * INTLAB * C-XSC * Flow* * Sollya * b4m * Interval Tools for ODEs and DAEs * Collection of Tools * MC++ * intpakX (Slides) * LdeApprox * ODEintegrator * List of Tools * HyTech = Formal Verification = * Deliverables - VEDECY * Parameter Synthesis for Hybrid Systems with an Application to Simulink Models * Automatic Verification And Analysis of Complex Systems People * Mitra Research Group * Cyberphysical Systems - Colorado * Hybrid Systems Group - ETHZ ** Software Tools * List of tools * Sage ** Interval Arithmetic * Python ** PyTaylor * CheckMate * d/dt * HSolver * Hybrid Toolbox * HyTech * Toolbox of Level Set Methods * KeYmaera * MATISSE * MPT Toolbox * PHAVer * SpaceEx * Passel * UPPAAL Academic * UPPAAL Commercial * Collection of Tools = Robust Control = * Industrial Robot Control System Parametric Design on the Base of Methods for Uncertain Systems Robustness * Robustness of model based simulations